@omkar
u must be crazy to call an IMO prob {VERY EASY} ;-)
. Let n be a positive integer and let a1, . . . , ak (k ≥ 2) be distinct
integers in the set{1, . . . , n} such that n divides ai(ai+1−1) for i = 1,
. . . , k−1. Prove that n does not divide ak( a1−1 ).